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More than 10,000 people have been killed over the past year, an activist group said

Syrian security fores pounded a densely populated Homs neighborhood Wednesday as the U.N. Security Council called on the government to work with its envoy to end the bloodshed.

At least 79 people were killed across Syria Wednesday, including 42 in Homs, according to the opposition Local Coordination Committees of Syria.

The LCC said at least 25 people slain in Homs were killed in the Khaldiya district, which had become a refuge in the devastated city for people fleeing other war-torn neighborhoods, such as Karm al Zaytoun, Bab Sbaa, Jib Jandali and Baba Amr.

The LCC said shelling and sniper gunfire rang out in Khaldiya as people pulled corpses from the streets. Dwellings there have been burned and destroyed, and there have been deaths and injuries. One man was killed by sniper fire, activists said. "Schools and mosques are also full of dozens of displaced residents from other neighborhoods. The trouble is, any small falling rocket can result in a real massacre," activist Abu Abdallah said.

LCC spokeswoman Rafif Jouejati said Khaldiya and other Homs neighborhoods such as Qusour are new targets for the regime. The group said regime forces firing at families fleeing Baba Amr killed two children.

"The majority of the remaining people there are women and children who were fleeing Baba Amr. The regime is now targeting ordinary civilians. FSA presence is no longer a pretext," she said, referring to the Free Syrian Army resistance.

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Homs has been a hotbed of anti-government sentiment during the yearlong uprising against President Bashar al-Assad's regime. Activists said 39 corpses were recovered from the city's Refaie district Wednesday. Abdallah said those people were killed around March 12.

U.N. officials say the yearlong crisis has killed more than 8,000 people, while opposition activists put the toll at more than 10,000, most of them civilians.

After months of failed attempts to stop the killings in Syria, the U.N. Security Council on Wednesday issued a presidential statement endorsing the peace mission of diplomat Kofi Annan, the U.N.-Arab League joint special envoy to Syria.

His mission is to stop the violence, gain "timely" humanitarian aid access and foster a Syrian-led political transition.

"The Security Council calls upon the Syrian government and opposition to work in good faith with the envoy towards a peaceful settlement of the Syrian crisis," the statement said.

Unlike resolutions, U.N. presidential statements aren't legally binding. But they do require unanimous support. This is significant because Russia and China, two permanent council members, have been obstacles to adopting tough resolutions on Syria.

In its statement, the council cited "its gravest concern at the deteriorating situation in Syria, which has resulted in a serious human rights crisis and a deplorable humanitarian situation" and expressed "profound regret at the death of many thousands of people in Syria."

"The Syrian government should immediately cease troop movements towards, and end the use of heavy weapons in, population centers, and begin pullback of military concentrations in and around population centers," the statement said.

"As these actions are being taken on the ground, the Syrian government should work with the envoy to bring about a sustained cessation of armed violence in all its forms by all parties with an effective United Nations supervision mechanism."

Annan, a former U.N. secretary-general, would seek "similar commitments" from the opposition and all relevant elements to stop the fighting and work with him to bring about a "sustained cessation of armed violence," the statement said.

The council called for a "daily two-hour humanitarian pause" for relief efforts and intensifying "the pace and scale of release of arbitrarily detained persons." It wants freedom of movement for journalists and "a nondiscriminatory visa policy for them."

It also urged respect for "freedom of association and the right to demonstrate peacefully."

U.S. Secretary of State Hillary Clinton called the council move a "positive step" and said "the council has now spoken with one voice."

In remarks directed at al-Assad, she said, "Take this path. Commit to it. Or face increasing pressure and isolation."

U.S. Ambassador to the U.N. Susan Rice called the U.N. presidential statement "a modest step" but "a step forward for the Security Council towards a more unified approach."

"Annan's proposal is the best way to put an end to the violence, facilitate much needed humanitarian assistance, and advance a Syrian-led political transition," she said.

U.N. Secretary-General Ban Ki-moon urged the government and opposition "to work in good faith" with Annan toward peace.

Russian Ambassador to the U.N. Vitaly Churkin said Russia "will support a Syrian-led political process, this is the aim of Kofi Annan's effort, and we will support whatever the outcome of that process might be."

Security Council members also issued a statement condemning deadly attacks this month in Damascus and Aleppo, two seats of power and support for the regime.

"The members of the Security Council reaffirmed that terrorism in all its forms and manifestations constitutes one of the most serious threats to international peace and security, and that any acts of terrorism are criminal and unjustifiable, regardless of their motivation, wherever, whenever and by whomsoever committed," the statement said.

The Syrian regime has blamed these attacks on terrorists, a claim disputed by rebels.

Two U.N. missions are under way in Syria. One comprises a team of experts discussing ways to implement the proposals laid out by Annan, and the other is a humanitarian team that -- along with the Organization of Islamic Cooperation -- is assessing the humanitarian needs in the country.

The United Nations, activists and human rights groups have documented widespread violations by Syrian government forces, including the use of torture, arbitrary detentions and indiscriminate shelling of neighborhoods.

Human Rights Watch said some anti-government forces have also committed abuses during the crisis, such as kidnappings, torture and executions. These allegations coincide with the emergence of armed resistance groups in recent months.

On Wednesday, a bomb targeting a military vehicle in the southern city of Daraa killed two Syrian soldiers, the opposition Syrian Observatory for Human Rights said. Security forces shot dead two civilians after the blast.

Syrian state-run media said Wednesday that "a number" of law-enforcement members and several civilians were killed Tuesday when a "suicide terrorist" set off a car explosion in the Daraa countryside.

The observatory also said a Syrian soldier was killed Wednesday during clashes in Hama, also in western Syria.

In the Damascus countryside city of Harasta, anti-regime Free Syrian Army fighters clashed with regime soldiers, the LCC said.

CNN cannot independently confirm reports of casualties or attacks in Syria because the government has severely restricted the access of international journalists.